Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

Abstract

Seven-degree-of-freedom redundant manipulators with link offset have many advantages, including obvious geometric significance and suitability for configu-ration control. Their configuration is similar to that of the experimental module manipulator (EMM) in the Chinese Space Station Remote Manipulator System. However, finding the analytical solution of an EMM on the basis of arm angle parameterization is difficult. This study proposes a high-precision, semi-analytical inverse method for EMMs. Firstly, the analytical inverse kinematic solution is established based on joint angle parameterization. Secondly, the analytical inverse kinematic solution for a non-offset spherical–roll–spherical (SRS) redundant manipulator is derived based on arm angle parameterization. The approximate solution of the EMM is calculated in accordance with the relationship between the joint angles of the EMM and the SRS manipulator. Thirdly, the error is corrected using a numerical method through the analytical inverse solution based on joint angle parameterization. After selecting the stride and termination condition, the precise inverse solution is computed for the EMM based on arm angle parameterization. Lastly, case solutions confirm that this method has high precision, and the arm angle parameterization method is superior to the joint angle parameterization method in terms of parameter selection.

Graphical abstract

Keywords

7-DOF redundant manipulator / inverse kinematics / semi-analytical / arm angle / link offset

References

[1] Yoshimitsu R, Yuguchi Y, Kobayashi A, . Dynamic simulator for HTV capture with Space Station Remote Manipulator System. In: Proceedings of the 12th International Symposium on Artificial Intelligence, Robotics and Automation in Space. Montreal: CSA, 2014, 1–8

[2] Rembala R, Ower C. Robotic assembly and maintenance of future space stations based on the ISS mission operations experience. Acta Astronautica, 2009, 65(7–8): 912–920

[3] Flores-Abad A, Ma O, Pham K, . A review of space robotics technologies for on-orbit servicing. Progress in Aerospace Sciences, 2014, 68: 1–26

[4] Sabatini M, Gasbarri P, Monti R, . Vibration control of a flexible space manipulator during on orbit operations. Acta Astronautica, 2012, 73(4–5): 109–121

[5] Nokleby S B. Singularity analysis of the Canadarm2. Mechanism and Machine Theory, 2007, 42(4): 442–454

[6] Coleshill E, Oshinowo L, Rembala R, . Dextre: Improving maintenance operations on the International Space Station. Acta Astronautica, 2009, 64(9–10): 869–874

[7] Boumans R, Heemskerk C. The European robotic arm for the international space station. Robotics and Autonomous Systems, 1998, 23(1–2): 17–27

[8] Krukewich K, Sexton J, Cavin K, . The systems engineering approach to the integration of the Space Station Remote Manipulator System on the International Space Station (ISS). Space Technology (Oxford, England), 1996, 16(1): 31–48

[9] Li D, Rao W, Hu C, . Overview of the Chinese Space Station manipulator. In: Proceedings of AIAA SPACE 2015 Conference and Exposition. Pasadena: AIAA, 2015, 1–6

[10] Liu H, Li Z, Liu Y, . Key technologies of TianGong-2 robotic hand and its on-orbit experiments. SCIENTIA SINICA Technologica, 2018, 48(12): 1313–1320 (in Chinese)

[11] Diftler M A, Mehling J S, Abdallah M E, . Robonaut 2—The first humanoid robot in space. In: Proceedings of the IEEE International Conference on Robotics and Automation. Shanghai: IEEE, 2011, 2178–2183

[12] Fukazu Y, Hara N, Kanamiya Y, . Reactionless resolved acceleration control with vibration suppression capability for JEMRMS/SFA. In: Proceedings of the IEEE International Conference on Robotics and Biomimetics. Bangkok: IEEE, 2009, 1359–1364

[13] Imaida T, Yokokohji Y, Doi T, . Ground-space bilateral teleoperation of ETS-VII robot arm by direct bilateral coupling under 7-s time delay condition. IEEE Transactions on Robotics and Automation, 2004, 20(3): 499–511

[14] Liu H, Jiang Z, Liu Y. Review of space manipulator technology. Manned Spaceflight, 2015, 21(5): 435–443 (in Chinese)

[15] Baillieul J. Avoiding obstacles and resolving kinematic redundancy. In: Proceedings of the IEEE International Conference on Robotics and Automation. San Francisco: IEEE, 1986, 1698–1704

[16] Guo D, Zhang Y. Acceleration-level inequality-based MAN scheme for obstacle avoidance of redundant robot manipulators. IEEE Transactions on Industrial Electronics, 2014, 61(12): 6903–6914

[17] Stevenson R, Shirinzadeh B, Alici G. Singularity avoidance and aspect maintenance in redundant manipulators. In: Proceedings of the 7th International Conference on Control, Automation, Robotics and Vision. Singapore: IEEE, 2002, 857–862

[18] Xu W, Zhang J, Liang B, . Singularity analysis and avoidance for robot manipulators with nonspherical wrists. IEEE Transactions on Industrial Electronics, 2016, 63(1): 277–290

[19] Hollerbach J M, Suh K C. Redundancy resolution of manipulators through torque optimization. In: Proceedings of the IEEE International Conference on Robotics and Automation. St. Louis: IEEE, 1985, 1016–1021

[20] Zhang Y, Li W, Yu X, . Encoder based online motion planning and feedback control of redundant manipulators. Control Engineering Practice, 2013, 21(10): 1277–1289

[21] Groom K N, Maciejewski A A, Balakrishnan V. Real-time failure-tolerant control of kinematically redundant manipulators. IEEE Transactions on Robotics and Automation, 1999, 15(6): 1109–1115

[22] Jamisola R S, Maciejewski A A, Roberts R G. Failure-tolerant path planning for kinematically redundant manipulators anticipating locked-joint failures. IEEE Transactions on Robotics, 2006, 22(4): 603–612

[23] She Y, Xu W, Su H, . Fault-tolerant analysis and control of SSRMS-type manipulators with single-joint failure. Acta Astronautica, 2016, 120: 270–286

[24] Singh G K, Claassens J. An analytical solution for the inverse kinematics of a redundant 7DoF manipulator with link offsets. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Taipei: IEEE, 2010, 2976–2982

[25] Seraji H. Configuration control of redundant manipulators: Theory and implementation. IEEE Transactions on Robotics and Automation, 1989, 5(4): 472–490

[26] Dubey R V, Euler J A, Babcock S M. Real-time implementation of an optimization scheme for seven-degree-of-freedom redundant manipulators. IEEE Transactions on Robotics and Automation, 1991, 7(5): 579–588

[27] Shah M, Patel R V. Inverse Jacobian based hybrid impedance control of redundant manipulators. In: Proceedings of the IEEE International Conference Mechatronics and Automation. Niagara Falls: IEEE, 2005, 55–60

[28] Colomé A, Torras C. Closed-loop inverse kinematics for redundant robots: Comparative assessment and two enhancements. IEEE/ASME Transactions on Mechatronics, 2015, 20(2): 944–955

[29] Lee S, Bejczy A K. Redundant arm kinematic control based on parameterization. In: Proceedings of the IEEE International Conference on Robotics and Automation. Sacramento: IEEE, 1991, 458–465

[30] Zu D, Wu Z, Tan D. Efficient inverse kinematic solution for redundant manipulators. Chinese Journal of Mechanical Engineering, 2005, 41(6): 71–75 (in Chinese)

[31] Kreutz-Delgado K, Long M, Seraji H. Kinematic analysis of 7-DOF manipulators. International Journal of Robotics Research, 1992, 11(5): 469–481

[32] Shimizu M, Kakuya H, Yoon W K, . Analytical inverse kinematic computation for 7-DOF redundant manipulators with joint limits and its application to redundancy resolution. IEEE Transactions on Robotics, 2008, 24(5): 1131–1142

[33] Xu W, Yan L, Mu Z, . Dual arm-angle parameterisation and its applications for analytical inverse kinematics of redundant mani-pulators. Robotica, 2016, 34(12): 2669–2688

[34] Zhou D, Ji L, Zhang Q, . Practical analytical inverse kinematic approach for 7-DOF space manipulators with joint and attitude limits. Intelligent Service Robotics, 2015, 8(4): 215–224

[35] Dereli S, Koker R. Calculation of the inverse kinematics solution of the 7-DOF redundant robot manipulator by the firefly algorithm and statistical analysis of the results in terms of speed and accuracy. Inverse Problems in Science and Engineering, 2020, 28(5): 601–613

[36] Faroni M, Beschi M, Pedrocchi N. Inverse kinematics of redundant manipulators with dynamic bounds on joint movements. IEEE Robotics and Automation Letters, 2020, 5(4): 6435–6442

[37] Gong M, Li X, Zhang L. Analytical inverse kinematics and self-motion application for 7-DOF redundant manipulator. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 18662–18674

[38] Kelemen M, Virgala I, Liptak T, . A novel approach for a inverse kinematics solution of a redundant manipulator. Applied Sciences, 2018, 8(11): 2229

[39] Crane C D III, Duffy J, Carnahan T. A kinematic analysis of the space station remote manipulator system (SSRMS). Journal of Robotic Systems, 1991, 8(5): 637–658

[40] Yu C, Jin M, Liu H. An analytical solution for inverse kinematic of 7-DOF redundant manipulators with offset-wrist. In: Proceedings of the IEEE International Conference on Mechatronics and Automation. Chengdu: IEEE, 2012, 92–97

[41] Abbasi V, Azria B, Tabarah E, . Improved 7-DOF control of ISS robotic manipulators. In: Proceedings of AIAA Space OPS 2004 Conference. Montreal: AIAA, 2004

[42] Lu S, Gu Y, Zhao J, . An iterative calculation method for solve the inverse kinematics of a 7-DOF robot with link offset. In: Huang Y, Wu H, Liu H, et al., eds. Intelligent Robotics and Applications. ICIRA 2017. Lecture Notes in Computer Science, vol 10464. Cham: Springer

[43] Jin M, Liu Q, Wang B, . An efficient and accurate inverse kinematics for 7-DOF redundant manipulators based on a hybrid of analytical and numerical method. IEEE Access: Practical Innovations, Open Solutions, 2020, 8: 16316–16330

[44] Xu W, Zhang J, Yan L, . Parameterized inverse kinematics resolution method for a redundant space manipulator with link offset. Journal of Astronautics, 2015, 36(1): 33–39 (in Chinese)

[45] Craig J J. Introduction to Robotics: Mechanics and Control. 4th ed. New York: Pearson Education Inc., 2005

Acknowledgements

This work was supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51521003) and the Major Research Plan of National Natural Science Foundation of China (Grant No. 91848202).

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